Geodesic
The Riemann–Roch theorem on surfaces with log terminal singularities
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 35-42 
A. B. Verevkin; Yu. G. Prokhorov. The Riemann–Roch theorem on surfaces with log terminal singularities. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 35-42. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a3/
@article{FPM_2004_10_4_a3,
     author = {A. B. Verevkin and Yu. G. Prokhorov},
     title = {The {Riemann{\textendash}Roch} theorem on surfaces with log terminal singularities},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {35--42},
     year = {2004},
     volume = {10},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a3/}
}
TY  - JOUR
AU  - A. B. Verevkin
AU  - Yu. G. Prokhorov
TI  - The Riemann–Roch theorem on surfaces with log terminal singularities
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2004
SP  - 35
EP  - 42
VL  - 10
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a3/
LA  - ru
ID  - FPM_2004_10_4_a3
ER  - 
%0 Journal Article
%A A. B. Verevkin
%A Yu. G. Prokhorov
%T The Riemann–Roch theorem on surfaces with log terminal singularities
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2004
%P 35-42
%V 10
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a3/
%G ru
%F FPM_2004_10_4_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Using the singular Riemann–Roch theorem, we propose a method to construct anticanonical sections on singular del Pezzo surfaces.

[1] Alekseev V. A., Nikulin V. V., “Klassifikatsiya poverkhnostei del Petstso s log-terminalnymi osobennostyami indeksa $2$, involyutsii na poverkhnostyakh K3 i gruppy otrazhenii v prostranstvakh Lobachevskogo”, Doklady po matematike i ee prilozheniyam, 2:2 (1988), 51–150 | MR

[2] Nikulin V. V., “Poverkhnosti del Petstso s log-terminalnymi osobennostyami, III”, Izv. AN SSSR. Ser. mat., 53:6 (1989), 1316–1334 | MR

[3] Prokhorov Yu. G., Shokurov V. V., “Pervaya osnovnaya teorema o dopolneniyakh: ot lokalnogo k globalnomu”, Izv. RAN. Ser. mat., 65:6 (2001), 99–128 | MR | Zbl

[4] Alexeev V., “Boundedness and $K^2$ for log surfaces”, Internat. J. Math., 5:6 (1994), 779–810 | DOI | MR | Zbl

[5] Blache R., “The structure of l.c. surfaces of Kodaira dimension zero, I”, J. Algebraic Geom., 4:1 (1995), 137–179 | MR | Zbl

[6] Keel S., McKernan J., Rational Curves on Quasi-Projective Surfaces, Memoirs AMS, 140, 1999 | MR

[7] Kojima H., “Logarithmic del Pezzo surfaces of rank one with unique singular points”, Japan. J. Math. (N.S.), 25:2 (1999), 343–375 | MR | Zbl

[8] Miyanishi M., Tsunoda S., “Logarithmic del Pezzo surfaces of rank one with contractible boundaries it infinity”, Japan. J. Math., 10 (1984), 271–319 | MR | Zbl

[9] Prokhorov Yu. G., Lectures on Complements on Surfaces, Memoirs Math. Soc. Japan, 10, 2001 | MR

[10] Reid M., “Young person's guide to canonical singularities”, Algebraic geometry (Bowdoin, 1985, Brunswick, Maine), Proc. Sympos. Pure Math., 46, Amer. Math. Soc., Providence, RI, 1987, 345–414 | MR

[11] Shokurov V. V., “Complements on surfaces”, J. Math. Sci., 102:2 (2000), 3876–3932 | DOI | MR | Zbl

[12] Zhang De-Qi, “Logarithmic Enriques surfaces, I”, J. Math. Kyoto Univ., 31:2 (1991), 419–466 | MR | Zbl